Vibrational zero-point energies

All geometrical optimizations were performed with the keywords tight and Int=UltraFine . The unsealed harmonic vibrational frequencies, zero-point vibrational energies (ZPVE), and enthalpies were also calculated. The ZPVE-corrected binding energies E , are reported throughout the work. 

There is a corresponding difference between two estimates of the bond distance in a molecule A—B. One. re, corresponds to the minimum in the energy distance curve (see figure). The second. r0, corresponds to the average distance in a molecule vibrating with zero-point energy. Since the curve is not perfectly parabolic the two values are not identical. 

Relative Energies, Zero Point Vibrational Energies... 

The isomers of C2H2 are 2Ol(s), acetylene and 2O2(s), vinylidene. Both have singlet ground states. A third isomer was reported to have appeared in a theoretical calculation, but, it turned out to have been a computational artifact [8]. Table 17.1 presents relative self consistent field (SCF) energies, zero point vibrational energies (ZPVE), and dipole moments of the isomers. 

Relative SCF Energies, Zero Point Vibrational Energies (ZPVE), and Dipole Moments of 201 (s) and 2O2(s)... 

In Table 17.12 we show relative SCF energies, zero point vibrational energies, and dipole moments of the open molecules. The quantum chemical treatments of the three open but branched constructs did not generate additional molecules. 

Relative SCF Energy, Zero Point Vibrational Energy (ZPVE), and Dipole Moment of the Open C5H2 Molecules... 

We will consider only two open molecules of C10H2, lOOl(s) and 10O2(s). Table 17.38 presents their relative energies, zero point vibrational energies and dipole moments. 

ZPE ZPVE zero point energy zero point vibrational energies ... 

In Table 1.1, the frequencies Vi[i = 1,2,3) correspond to the transition from the ground state (of all the vibrational modes) to the first vibrational level of the ith mode of vibration. The zero point energy of H2O and of D2O are also given in Table 1.1. For more details, see Eisenberg and Kauzmann (1969). 

BeO and H2. If, however, the first vibrational levels (zero-point energies) are compared instead, this difference becomes about 1.0 eV. 

Here tSEehc, tSZPVE, Er and A5 are the diiferences in electronic energy, zero-point vibrational energy, thermal energy and entropy between the products and reactants, respectively. To calculate these thermodynamic parameters, the basic thermochemical quantity is the partition function q(F,7), which is the corresponding quantity of the total partition function Q in volume V. The total partition function Q is the product of partition functions for translation, rotation, vibration and electronic degrees of freedom. 

Molecules are composed of multiple atoms that are bonded by covalent bonds. Quantum mechanics indicates that those atoms are constantly vibrating about some equilibrium position, even at absolute zero, having some nonzero minimum energy of vibration (the zero-point energy ). Because vibrational motions of molecules represent another form of energy, we can define a vibrational partition function q, for a molecule such that... 

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